Geometry Puzzle – Challenge 64
How many minutes does it take an hour hand to sweep 540 degrees? The hour hand moves 30 degrees per hour, so 540 degrees is 18 hours, which is 1080 minutes. The trick is connecting the angle-per-hour rate (30 degrees/hour) to the question.
Key takeaways:
- A clock has 12 hour sections; 360/12 = 30 degrees per section.
- Hour hand moves 30 degrees per hour, or 0.5 degree per minute.
- 540 / 30 = 18 hours.
- 18 hours times 60 minutes/hour = 1080 minutes.
- Always link the angle question to the hand-speed rate first.
A perfect geometry and measurement-related puzzle to tease your brain and help you have a good time while reviewing a math concept! For additional educational resources
Challenge:
How many minutes does it take an hour hand of a clock to move \(540^o\)?
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The correct answer is 1080 minutes.
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A clock has 12 sections from 1 to 12. An hour hand of a clock moves 30 degree in one hour.
360 ÷ 12 = 30
540 ÷ 30 = 18
It takes 18 hours (or 18 × 60 = 1080 minutes) an hour hand of a clock to move \(540^o\).The Best Books to Ace Algebra
Frequently Asked Questions
How many degrees does the hour hand move in 1 minute?
The hour hand moves 0.5° per minute. It turns 30° every hour, and 30 ÷ 60 = 0.5. This rate solves the 540° puzzle directly: 540 ÷ 0.5 = 1080 minutes, which matches 18 hours × 60 minutes. So if you know a turn in degrees, divide by 0.5 to get the minutes it takes.
How many degrees does the hour hand move in 1 hour?
The hour hand moves 30° in 1 hour. A full circle is 360°, and the hour hand takes 12 hours to go around, so 360 ÷ 12 = 30. That is why 540° takes 540 ÷ 30 = 18 hours: one full trip around the clock (12 hours) plus half a trip (6 hours).
How many degrees does the hour hand move in 20 minutes?
The hour hand moves 10° in 20 minutes, because 20 × 0.5 = 10. Using the same rate, it moves 7.5° in 15 minutes, 15° in 30 minutes and 22.5° in 45 minutes. These small shifts matter in clock problems: at 4:20, the hour hand has moved 10° past the 4.
How many degrees does the hour hand move in 1 second?
The hour hand moves 1/120 of a degree per second, about 0.0083°. It moves 0.5° per minute, and dividing by 60 seconds gives 0.5 ÷ 60 = 1/120. It is far too slow to see, yet over 1080 minutes it still adds up to the 540° in this puzzle.
How many degrees does the minute hand move in 20 minutes?
The minute hand moves 120° in 20 minutes. It goes all the way around, 360°, in 60 minutes, so it moves 6° per minute, and 20 × 6 = 120. That is 12 times as fast as the hour hand, which moves only 10° in the same 20 minutes.
How many degrees does the minute hand move in 1 second?
The minute hand moves 0.1° per second. It moves 6° each minute, and 6 ÷ 60 = 0.1. Compare that with the second hand, which moves 6° every second. In the 1080 minutes it takes the hour hand to sweep 540°, the minute hand turns 1080 × 6 = 6480°, or 18 full circles.
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If your student enjoys puzzles like this, Geometry for Beginners works the same kinds of relationships inside a full curriculum. Pre-Algebra for Beginners covers the algebraic foundations.
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